details

property	value
status	complete
benchmark	z078.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0990909 seconds
cpu usage	0.084285
user time	0.027718
system time	0.056567
max virtual memory	113188.0
max residence set size	5548.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x1:S) (RULES d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S ) Problem 1: Innermost Equivalent Processor: -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: D(s(x1:S)) -> D(p(s(x1:S))) D(s(x1:S)) -> P(s(x1:S)) F(s(x1:S)) -> D(f(p(s(x1:S)))) F(s(x1:S)) -> F(p(s(x1:S))) F(s(x1:S)) -> P(s(x1:S)) -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S Problem 1: SCC Processor: -> Pairs: D(s(x1:S)) -> D(p(s(x1:S))) D(s(x1:S)) -> P(s(x1:S)) F(s(x1:S)) -> D(f(p(s(x1:S)))) F(s(x1:S)) -> F(p(s(x1:S))) F(s(x1:S)) -> P(s(x1:S)) -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: D(s(x1:S)) -> D(p(s(x1:S))) ->->-> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S ->->Cycle: ->->-> Pairs: F(s(x1:S)) -> F(p(s(x1:S))) ->->-> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: D(s(x1:S)) -> D(p(s(x1:S))) -> Rules: d(0(x1:S)) -> 0(x1:S) d(s(x1:S)) -> s(s(d(p(s(x1:S))))) f(0(x1:S)) -> s(0(x1:S)) f(s(x1:S)) -> d(f(p(s(x1:S)))) p(s(x1:S)) -> x1:S -> Usable rules: p(s(x1:S)) -> x1:S ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 popout

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actions

all output return to SRS Standard